Massachusetts Attorney General Martha Coakley sent a letter to the trustees of the MBTA Retirement Fund on Monday, urging them to “act expeditiously to increase transparency in the board’s operations,’’ and adopt ethical and disclosure rules in line with other pension funds for public workers.

Coakley since December has been investigating a $25 million investment by the pension fund that went bad. In her letter, a copy of which was obtained by the Globe, Coakley said the board should embrace new rules related to conflicts of interest, financial disclosures, and disclosing records to the public.

“There is a strong public interest in the board taking action to increase transparency,’’ Coakley wrote, “because a significant portion of the MBTA’s overall revenues come from fares paid by transit riders, dedicated sales tax revenues, and assessments on cities and towns within the MBTA service area.’’

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The letter came on the eve of a public hearing scheduled by the Massachusetts Legislature to examine the same issues at the pension board. The $1.6 billion T pension fund has been under scrutiny since December, when its failed $25 million investment in a Fletcher Asset Management hedge fund came to light in news reports.

The hedge fund is now bankrupt as the result of a suspected fraud at New York-based Fletcher. The man who sold the Fletcher investment to the pension fund was Karl White—the former executive director of the pension fund, who had left to work for Fletcher in 2006. If the fund followed the ethics rules that apply to state agencies, it would not have been able to business with Fletcher for at least a year.

Fletcher is under investigation by the FBI and the Securities and Exchange Commission.

All six members of the pension fund board, led by chairwoman Janice Loux, have been invited to testify at the Tuesday hearing. The Joint Committee on Public Service asked 18 people to attend in all, including MBTA General Manager Beverly Scott and Massachusetts Department of Transportation secretary Richard Davey.

The board is currently split in half over whether to start disclosing records. In a vote last month, Loux, T deputy general manager Jonathan Davis, and Urban League of Eastern Massachusetts chief Darnell Williams all voted to disclose. The three union members on the board voted no. In a tie-breaking vote, honorary board member Katherine Hesse, an attorney, also voted no.

A spokesman for the MBTA pension fund was not immediately available for comment. It is unknown whether the fund’s directors will show up at the meeting. All but one—the T’s Davis—have refused to be interviewed.

Coakley suggested that new legislation may be necessary to force the board to comply with new rules. But in her letter, she appears to be suggesting that the board voluntarily adopt ethics and disclosure rules in line with the state pension fund, for instance.

The board has been relying on its status as a private trust to avoid holding public meetings, making its records public, and establishing typical ethics protocols. A 1993 Supreme Judicial Court ruling affirmed their view that as a private trust, they are not subject to public oversight. And the Secretary of State’s office so far has agreed with that view.

Still, Coakley wrote, “We believe that increased transparency and protections against conflict of interest are beneficial to the T employees and the public.’’